Determine the equation of the line that passes through the point (-1, 2) and isperpendicular to the line y = -2.
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1) In this question, let's find the equation, using the point-slope formula:
[tex](y-y_0)=m(x-x_0)[/tex]2) Notice that since we want a perpendicular line we can write a perpendicular line to y=2, as x=-1/2 for -1/2 is the opposite and reciprocal to 2 (the necessary condition to get a perpendicular line).
So, the slope of that perpendicular line is -1/2
3) Let's plug into that Point-Slope formula, the slope m= -1/2 and the point:
[tex]\begin{gathered} (y-2)=-\frac{1}{2}(x+1) \\ y-2=-\frac{1}{2}x-\frac{1}{2} \\ y=-\frac{1}{2}x-\frac{1}{2}+2 \\ y=-\frac{1}{2}x+\frac{3}{2} \end{gathered}[/tex]4) Thus, the answer is:
[tex]y=-\frac{1}{2}x+\frac{3}{2}[/tex]Related Questions
in the triangle abc a =65 b =58 identity the longest side of the triangle
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We know two angles of a triangle, ∠A = 65° and ∠B = 58°, and we have to identify the longest side.
The longest side will be the one that is opposite to the widest angle. In our case, we don't know the measure of C, but we know that the sum of the three measures has to be 180°, so we can calculate it as:
[tex]\begin{gathered} m\angle A+m\angle B+m\angle C=180\degree \\ 65+58+m\angle C=180 \\ m\angle C=180-65-58 \\ m\angle C=57\degree \end{gathered}[/tex]As the widest angle is at vertex A, the longest side will be its opposite, which correspond to the side formed by the other two vertices: B and C.
The longest side is BC.
PART E.)In terms of the trigonometry ratios for triangle BCD, what is the length of line BD. Insert text on the triangle to show the length of line BD. When you’re done use the formula for the area of a triangle area equals 1/2 times base times height write an expression for the area of triangle ABC this when you do this base your answer on what u did in part E
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Sine formula
[tex]\sin (angle)=\frac{\text{opposite side}}{hypotenuse}[/tex]Considering angle C from triangle BCD, the opposite side is side BD and the hypotenuse is side BC which length is a units. Then:
[tex]\begin{gathered} \sin (\angle C)=\frac{BD}{a} \\ \text{ Isolating BD} \\ \sin (\angle C)\cdot a=BD \end{gathered}[/tex]The area of a triangle is calculated as follows:
[tex]A=\frac{1}{2}\cdot\text{base}\cdot\text{height}[/tex]In triangle ABC the base is b units long and its height is segment BD, then the area of triangle ABC is:
[tex]\begin{gathered} A=\frac{1}{2}\cdot b\cdot BD \\ \text{ Substituting with the previous result:} \\ A=\frac{1}{2}\cdot b\cdot a\cdot\sin (\angle C) \end{gathered}[/tex]
F(x)=2|x-1| Graph using transformations and describe the transformations of the parent function y =x^2.
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[Please see that in the question should be a mistake regarding the parent function. It should be written y = |x| instead of y = x².]
To answer this question, we need to know that the below function is a transformation of the parent function, f(x) = |x|:
[tex]f(x)=2|x-1|[/tex]Describing the transformationsTo end up with the above function from the parent function, we need to follow the next steps:
1. Translate the function, y = |x| one unit to right. We can do this by subtracting one unit to the parent function as follows:
[tex]f(x)=|x-1|[/tex]We can see this graphically as follows:
The blue function is the first transformation of the parent function, f(x) = |x|.
2. The function has been dilated by a factor of 2 from the x-axis. That is, the function has been dilated by a factor of 2 vertically. Then, we have:
[tex]f(x)=2|x-1|[/tex]And now, we can see the transformation graphically as follows:
Therefore, the blue line is the graph representation of the function:
[tex]f(x)=2|x-1|[/tex]find the mean median and mode Numbers 1,2,2,6,5,1,1
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Solution:
We are required to find the mean median and mode of 1,2,2,6,5,1,1.
[tex]Mean=\frac{1+2+2+6+5+1+1}{7}=\frac{18}{7}=2.5714[/tex]Median:
Sort the data
1, 1, 1, 2, 2, 5, 6
The median = 2
Mode = 1 (because it appears the most (3 times) )
Amount of Water (ml) 5 8 8.5 8 8.ŏ 8 8 8 10 I → 0 1 2 3 4 5 6 7 8 9 Days What information does the intercept provide A The amount of water in the beaker decreased by 40 ml. B. The water was gone by the eighth day.
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First, we need to identify the y-intercept that is the value of the coordinate y when the coordinate is 0 in this case our y-intercept is in 40
The y-intercept provide the start amount of water therefore the correct choice is D. the water level started at 40 mL
(3m + n )(3m − n )solve by using foil
Answers
Given: The expression below
[tex](3m+n)(3m-n)[/tex]To: Solve using foil
Solution
foil means
F---- FIRST
O- OUTER
I ---- INNER
L ----- LAST
Let us apply the foil method
Therefore,
[tex]\begin{gathered} (3m+n)(3m-n) \\ =3m\times3m+3m\times-n+n\times3m+n\times-n \\ =9m^2-3mn+3mn-n^2 \\ -3mn+3mn=0 \\ Therefore \\ (3m+n)(3m-n)=9m^2-n^2 \end{gathered}[/tex]Hence, the solution is
9m² - n²
graph the quadrilateral with the given vertices in a coordinate plane. then show the quadrilateral in a a parallelogram
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First, let's graph the polygon:
Now, let's prove it's a parallelogram by showing that the segments NP and RQ are parallel, and NR and PQ are parallel as well.
Let's prove that the angular coefficient is the same for NR and PQ
[tex]\begin{gathered} m_{NR}=\frac{0-(-4)}{-5-(-3)}=-\frac{4}{3} \\ \\ m_{PQ}=\frac{5-0}{0-3}=-\frac{4}{3} \end{gathered}[/tex]Then they're parallel, just to confirm, let's do the same for NP and RQ
[tex]\begin{gathered} m_{NP}=\frac{4-0}{0-(-5)}=\frac{4}{5} \\ \\ m_{RQ}=\frac{-4-0}{-2-(3)}=\frac{4}{5} \end{gathered}[/tex]Then it's parallel as well.
Countries represented at each festival 6 5 4 Number of festivals 3 N 1 0 0-5 6-11 12-17 18-23 24-29 Number of countries How many festivals had 12 or more countries represented.
Answers
11 festivals
Explanation
to find the nunmber of festivals that had 12 or more countries, sum the festivals for all values in number of countries greather than 12, it its
[tex]\begin{gathered} \text{column 3 (12-17)=5 festivals} \\ \text{column 4(18-23)=4 festivals} \\ column5(24-29)=2\text{ festivals} \\ so,\text{ the total of festivals for 12 or more countries is} \\ \text{total}=5+4+2 \\ total=11\text{ festivals} \end{gathered}[/tex]I hope this helps you
I’m stuck I don’t know what I’m doing at all help me out??
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Point: (x,y) = (-4,8)
We have to graph the point and set a vertical line.
Line equation:
x= -4
For any value of x, it always will be -4.
8 singles, 10 fives, 2 twenties, and 3 hundred dollar bills are all placed in a hat. If a player is to reach into the hat and randomly choose one bill, what is the fair price to play this game?
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The total number of bills are 23.
The probability to get single = 8/23
The probability to get five = 10/23
The probability to get twenty = 2/23
The probability to get a hundred = 3/23
So, the fair price to play this game is calculated below:
[tex]\begin{gathered} \text{fair price}=1\times\frac{8}{23}+5\times\frac{10}{23}+20\times\frac{2}{23}+100\times\frac{3}{23} \\ =\frac{8}{23}+\frac{50}{23}+\frac{40}{23}+\frac{300}{23} \\ =\frac{8+50+40+300}{23} \\ =\frac{398}{23} \\ =17.30 \end{gathered}[/tex]Thus, the fair price to play this game is $17.30
50 points!
What is the value of x?
Enter your answer in the box.
x =
Answers
Answer:
x = 3
Hope this helps!
Step-by-step explanation:
ΔABC is a 45°, 45°, 90° triangle. The longest side ( 6[tex]\sqrt{2}[/tex] ) can be [tex]x\sqrt{2}[/tex] while AB and CB are x. Because 6[tex]\sqrt{2}[/tex] is equal to [tex]x\sqrt{2}[/tex], you can see that x is equal to 6. Both AB and CB are equal to 6. ΔBDC ( CDB ) is a right triangle ( 30°, 60°, 90° ) so, BD = x, CB = 2x, and CD = [tex]x\sqrt{3}[/tex]. CB is equal to 6 so 2x = 6, x = 3.
12 Stefanie is painting her bedroom. She can paint 12 1/3 square feet in 1/5 of an hour. How many square feet can she paint in one hour?
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stephanie can paint 12 1/3 square feet in 1/5 of an hour. So,
[tex]undefined[/tex]step by step on how to solve 3/4 - 1/2 × 7/8
Answers
EXPLANATION
Given the following operation:
3/4 - 1/2*7/8
First, let's solve 1/2*7/8:
Multiply fractions: a/b* c/d = (a*c)/(b*d)
[tex]=\frac{1\cdot7}{2\cdot8}[/tex]Multiply the numbers: 1*7 = 7
[tex]=\frac{7}{2\cdot8}[/tex]Multiply the numbers 2*8=16
[tex]=\frac{3}{4}-\frac{7}{16}[/tex]Now, we need the Least Common Multiplier of 4, 16:
The LCM of a, b is the samllest positive number that is divisible by both a and b:
Prime factorization of 4:
4 divides by 2 ---> 4= 2*2
2 is a primer number, therefore no further factorization is possible.
Prime factorization of 16:
Multiply each factor the greatest number of times it occurs in either 4 or 16
= 2*2*2*2
Multiply the numbers: 2*2*2*2 = 16
Adjust fractions based on LCM
For 3/4: multiply the denominator and numerator by 4
[tex]\frac{3}{4}=\frac{3\cdot4}{3\cdot4}=\frac{12}{16}[/tex][tex]=\frac{12}{16}-\frac{7}{16}[/tex]Since the denominators are equal, combine the fractions:
[tex]=\frac{12-7}{16}[/tex]Subtract the numbers: 12-7 = 5
[tex]=\frac{5}{16}[/tex]convert 62°F to degree Celsius if necessary round to the nearest 10th of a degreeC=5/9 (F-32)F=9/5 C + 32
Answers
Given the following question:
Using the formula:
[tex]undefined[/tex]2500/10.5 please show work
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The given expression is
2500/10.5
We would multiply the numerator and denominator by 10. We have
2500 x 10/10.5 x 10
= 25000/105
We would divide the numerator and denominator by common factors until they can't be simplified further. Dividing by 5, we have
5000/21
It can't be simplified further since there is no common factor of 5000 and 21. We would convert the fraction to mixed fraction
5000/21 = 238 remainder 2
Thus, if we write it as mixed fraction, we have
238 2/21
3x+2y=10 table of ordered pair
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Answer:
Step-by-step explanation:
for sure
69 is _________% more than 60
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To find the solution we can use the rule of three:
[tex]\begin{gathered} 60\rightarrow100 \\ 69\rightarrow x \end{gathered}[/tex]then:
[tex]\begin{gathered} x=\frac{69\cdot100}{60} \\ x=115 \end{gathered}[/tex]This means that 69 is 115% of 60.
Therefore 69 is 15% more than 60.
the letter "t" estimated makes up 10% of a language. a random sample of 700 letters is taken from a book. what is the approximate probability that the random sample of 700 letters will contain 8.9% t's
Answers
In this problem, we have a Binomial Probability Distribution
so
n=700
x=700*(8.9/100)=62.3=62
[tex]P(x=62)=\frac{700!}{62!(700-62)!}\cdot0.10^{(62)}\cdot0.90^{(700-62)}[/tex]P(x=62)=0.0313
the aprroximate probability is 3.13%Estimate the amount of money he will have after paying these bills each month
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First, add all those bills.
[tex]undefined[/tex]queremos hacer una tetra brik de base cuadrada de 8cm de lado y con capacidad de 2l¿cuanto cartón necesitaremos ?
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transformamos las unidades de litros a centimetros cubicos, esto es:
1 L = 1000 cm3
2L = 2000 cm3
hallamos el area de la base
[tex]A=L^2=8^2=64cm^2[/tex][tex]\begin{gathered} V=A\times h \\ 2000=64\times h \\ \frac{2000}{64}=\frac{64h}{64} \\ h=31.25 \end{gathered}[/tex]hallamos el area lateral
[tex]Alateral=P\times h=(4\times8)\times31.25=32\times31.25=1000cm^2[/tex]luego el area total
[tex]\text{Atotal}=2Abase+Alateral=2(64)+1000=128+1000=1128\operatorname{cm}[/tex]respuesta: se necesitan 1128 cm2 de carton
A triangle is formed by three roads that connect Shelbyville, Springfield, and Capitol City together. These roads are 19, 21, and 24 miles long. This forms a(n) _______ triangle.
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Given:
A triangle is formed by three roads that connect Shelbyville, Springfield, and Capitol City together.
These roads are 19, 21, and 24 miles long.
So, as we can see the three sides are different in lengths
So, the answer will be:
This forms a scalene triangle.
find f such that the given conditions are satisfiedf’(x)=x-4, f(2)=-1
Answers
Given:
[tex]f^{\prime}\left(x\right)=x-4,\text{ and}f\left(2\right)=-1[/tex]To find:
The correct function.
Explanation:
Let us consider the function given in option D.
[tex]f(x)=\frac{x^2}{2}-4x+5[/tex]Differentiating with respect to x we get,
[tex]\begin{gathered} f^{\prime}(x)=\frac{2x}{2}-4 \\ f^{\prime}(x)=x-4 \end{gathered}[/tex]Substituting x = 2 in the function f(x), we get
[tex]\begin{gathered} f(2)=\frac{2^2}{2}-4(2)+5 \\ =2-8+5 \\ =-6+5 \\ f(2)=-1 \end{gathered}[/tex]Therefore, the given conditions are satisfied.
So, the function is,
[tex]f(x)=\frac{x^{2}}{2}-4x+5[/tex]Final answer: Option D
Which equation has (1,1),(2,4),(3,7) and (4,10) as solutions?A)y=2x - 1.B)y= 2x+3.C)y=3x-2.D)y=3x+1.
Answers
Answer:
y=3x-2
Explanation:
The equation that has the given solutions is the equation that satisfies all the given (x, y) pairs.
From the given options:
[tex]\begin{gathered} \text{When x=1} \\ y=3x-2 \\ y=3(1)-2=1 \\ \implies(1,1) \end{gathered}[/tex]Likewise:
[tex]\begin{gathered} \text{When x=}2 \\ y=3x-2 \\ y=3(2)-2=4 \\ \implies(2,4) \end{gathered}[/tex]Also when x=3:
[tex]\begin{gathered} y=3\mleft(3\mright)-2=7 \\ \implies(3,7) \end{gathered}[/tex]Finally, when x=4
[tex]\begin{gathered} y=3\mleft(4\mright)-2=10 \\ \implies(4,10) \end{gathered}[/tex]Thus, since y=3x-2 satisfies all four points, it is the right equation.
A group of five will rent a car for a spring break trip and divide the costs associated with the car among them. The rental costs $480 for the week. Insurance is an additional $175, they estimated they’ll use 120 gallons of gas, and gas costs around $2.80 per gallon. Estimate how much each friend will pay for the cost associated with the car
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Solution:
Given:
[tex]\begin{gathered} car\text{ rental cost}=\text{ \$}480 \\ Insurance=\text{ \$}175 \\ Gas=120\times2.80=\text{ \$}336 \end{gathered}[/tex]Thus, the total cost associated with the car is;
[tex]480+175+336=\text{ \$}991[/tex]Each friend will pay;
[tex]\frac{991}{5}=\text{ \$}198.20[/tex]Therefore, each friend will pay $198.20
units givenQuestion 2 (3 points)toUsing the Rectangular Prism in the picture, find the Lateral Area, the Area of a Single Base,and the TOTAL Surface Area:.12 cm825 cm10 cmUse the face with dimensions 10cm x 5cm as the base.Lateral Area =cm²Single Base Area =64188 in48cm²
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Solution:
Given the rectangular prism;
Where;
[tex]\begin{gathered} length,l=10cm \\ \\ width,w=5cm \\ \\ height,h=2cm \end{gathered}[/tex]Thus, the lateral area, L is;
[tex]\begin{gathered} L=2(l+w)h \\ \\ L=2(10+5)2 \\ \\ L=4(15) \\ \\ L=60cm^2 \end{gathered}[/tex]ANSWER:
[tex]Lateral\text{ }Area=60cm^2[/tex]Also, the single base area, B, is;
[tex]\begin{gathered} B=l\times w \\ \\ B=10\times5 \\ \\ B=50cm^2 \end{gathered}[/tex]ANSWER:
[tex]Single\text{ }Base\text{ }Area=50cm^2[/tex]Then, the surface area, S, is;
[tex]\begin{gathered} S=L+2B \\ \\ S=60+2(50) \\ \\ S=60+100 \\ \\ S=160cm^2 \\ \\ \end{gathered}[/tex]ANSWER:
[tex]Surface\text{ }Area=160cm^2[/tex]Jeff picks a number with 2 tens 42 ones. victor picks a number with 3 tens 51 ones. what number does each child pick?
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Jeff = 2 tens 42 ones
Victor = 3 tens 51 ones
what number is = ?
Step 02:
Jeff = 2 tens 42 ones
2 * 10 = 20
42 * 1 = 42
----------
Victor = 3 tens 51 ones
Answer:
Jeff: 62
Victor: 81
Step-by-step explanation:
Jeff has a number with 2 tens, and 42 ones. We can write out our 2 tens like this: 10 + 10 = 20
Next, he has 42 ones. This is just another way of saying '42'
So, jeff picked a number that is 20 + 42 = 62
Now, Victor. Victor has a number with 3 tens. This is saying: 10 + 10 + 10 which is 30. He has 51 ones, which is just the number 51.
So, Victor's number is 30 + 51 = 81
Which best represents the transformations for the coordinates of the verticals of the given pairs of triangles (1,6), (-1,3), (5,2), and (-1,6), (-3,3), (3,2) Is it a rotation (that my educated guess)Reflection or translation?
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No. It's not a rotation. It's translation.
for translation, there is a formula that is
[tex]x^{\prime}=x+a\text{ }[/tex]and
[tex]y^{\prime}=b+y[/tex][tex]y^{\prime}=b+y[/tex]where (x',y') is the new coordinate and (x,y) is the old one and (a,b) is the increasing value of (x,y)
so here we have the new coordinates are (-1,6), (-3,3), (3,2)
and the olds are (1,6), (-1,3), (5,2)
[tex]\begin{gathered} -1=a+1 \\ and\text{ }6=b+6 \\ this\text{ gives } \\ a=(-2)\text{ and b=0} \\ similarly\text{ you take each case you will get the value of a is \lparen-2\rparen and the value of b is 0.} \end{gathered}[/tex]Thus we can say that the triangle is translated by adding the horizontal value (a) =(-2) to the x-coordinate of each vertex and the vertical value (b)=0 to the y-coordinate.
now you can see
[tex]\begin{gathered} 1+(-2)=1\text{ \& 6+\lparen0\rparen=6 ie \lparen1,6\rparen+\lparen-2,0\rparen=\lparen-1,6\rparen} \\ similarly \\ (-1,3)+(-2,0)=(-3,3) \\ (5,2)+(-2,0)=(3,2) \end{gathered}[/tex]so the right answer is translation.
let f(x)=2x+1. write a function g(x) whose grass is a rotation of f (x) about (0,1) by a factor of 3 , followed buy a vertical translation 6 units down
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1) Considering f(x)= 2x+1, And g(x) be f(x) rotated about y=1, with a factor of 3 this
A vertical translation 6 units down= g(x) = 2x -5
A factor of 3: g(x)= 3(2x)-5
Given cos = 0.9528, find .
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Given:
[tex]\cos \theta=0.9528[/tex]To find the value of θ,
[tex]\begin{gathered} \cos \theta=0.9528 \\ \theta=\cos ^{-1}(0.9528) \\ \theta=17.6739^{\circ} \end{gathered}[/tex]
Determine the radius of the circle with center at (7,-4) and a point on the circle (-2, 5). Show organized work to support your answer. Round your answer to the nearest tenth.
Answers
The radius of the circle with center at (7,-4) and a point on the circle (-2, 5). is 9√2
Radius is the line segment extending from the center of a circle or sphere to the circumference or bounding surface, it is the distance betwee the center of the circle to a point on the circumference
the circle with center at (7,-4) and a point on the circle (-2, 5).
We can find the radius by using the distance formula
r = √((x₂ - x₁)² + (y₂ - y₁)²)
r = √((-2 -7)² + 5 - (-4)²)
r = √(9² + 9²)
r = 9√2
Therefore, the radius of the circle with center at (7,-4) and a point on the circle (-2, 5). is 9√2
To learn more about distance refer here
https://brainly.com/question/7243416
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